A Computational Quantum Chemical Study of the Bonded Interactions in Earth Materials and Structurally and Chemically Related Molecules

Gibbs, G. V.; Boisen, M. B.; Beverly, Lesa L.; Rosso, Kevin M.

doi:10.2138/rmg.2001.42.10

Cited by 34 publications

(37 citation statements)

References 129 publications

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“…13 The relationship between the distance between r c and the nodal surface has not been examined to our knowledge for the remaining second row M-O interactions. Figure 3a shows that the local electronic energy density H(r c ) tends to decrease with decreasing M-O bond lengths as expected from the trends displayed in Figures 1a and 2a and as calculated for the M-O and M-N bonded interactions for the molecules studied by Hill et al, 30 Feth et al, 31 and Gibbs et al 19,32,33 The decrease in H(r c ) is relatively small for the M-O bonded interaction involving the more electropositive M atoms (Figure 3a), but it decreases more rapidly for the interactions involving the more electronegative atoms. The small positive H(r c ) values for the Na-O and Mg-O interactions can be explained in terms of the small magnitudes of G(r c ) and V(r c ), both of which approach zero as the bonds adopt lengths of 1.75 Å and longer.…”

Section: Introductionsupporting

confidence: 68%

Bond Length and Local Energy Density Property Connections for Non-Transition-Metal Oxide-Bonded Interactions

et al. 2006

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For a variety of molecules and earth materials, the theoretical local kinetic energy density, G(r(c)), increases and the local potential energy density, V(r(c)), decreases as the M-O bond lengths (M = first- and second-row metal atoms bonded to O) decrease and the electron density, rho(r(c)), accumulates at the bond critical points, r(c). Despite the claim that the local kinetic energy density per electronic charge, G(r(c))/rho(r(c)), classifies bonded interactions as shared interactions when less than unity and closed-shell when greater, the ratio was found to increase from 0.5 to 2.5 au as the local electronic energy density, H(r(c)) = G(r(c)) + V(r(c)), decreases and becomes progressively more negative. The ratio appears to be a measure of the character of a given M-O bonded interaction, the greater the ratio, the larger the value of rho(r(c)), the smaller the coordination number of the M atom and the more shared the bonded interaction. H(r(c))/rho(r(c)) versus G(r(c))/rho(r(c)) scatter diagrams categorize the M-O bonded interactions into domains with the local electronic energy density per electron charge, H(r(c))/rho(r(c)), tending to decrease as the electronegativity differences for the bonded pairs of atoms decrease. The values of G(r(c)) and V(r(c)), estimated with a gradient-corrected electron gas theory expression and the local virial theorem, are in good agreement with theoretical values, particularly for the bonded interactions involving second-row M atoms. The agreement is poorer for shared C-O and N-O bonded interactions.

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Section: Introductionsupporting

confidence: 68%

Bond Length and Local Energy Density Property Connections for Non-Transition-Metal Oxide-Bonded Interactions

et al. 2006

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“…Burdett and Hawthorne (1993), for instance, related key aspects of the BVM to molecular orbital theory. Gibbs has long argued for using Bader's Atoms in Molecules (AIM) theory as a basis for rationalizing the BVM (Gibbs et al 2001(Gibbs et al , 2014.…”

Section: Introductionmentioning

confidence: 99%

“…One promising avenue is the Quantum Theory of Atoms in Molecules (QTAIM or AIM) of Bader (Bader 1991;Popelier 2000), which provides an intriguing method for reducing the complex electron density distributions in molecules and crystals to a manageable set of descriptors that have been shown to be quite useful for rationalizing chemical structure and reactivity. Gibbs and coworkers (Gibbs et al 2001(Gibbs et al , 2003(Gibbs et al , 2004(Gibbs et al , 2006(Gibbs et al , 2008a(Gibbs et al , 2008b(Gibbs et al , 2014 have demonstrated a strong correlation between bond valence and one of the primary AIM descriptors, the bond critical point electron density, in oxide crystals and some analogous molecules. If so, this suggests that one could use this relationship by way of analogy to generate hypotheses about the proper form of the bond valence-length relationship.…”

Section: Introductionmentioning

confidence: 99%

AIM analysis and the form of the bond-valence equation

Wander

Bickmore

Lind

et al. 2014

American Mineralogist

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The bond-valence model (BVM) posits an inverse relationship between bond valence (essentially bond order) and bond length, typically described by either exponential or power-law equations. To assess the value of these forms for describing a wider range of bond lengths than found in crystals, we first assume that the bond critical point density (r b , reported in e -/Å 3 ) is at least roughly proportional to bond valence. We then calculate r b -distance curves for several diatomic pairs using electronic structure calculations (CCSD/aug-cc-pVQZ) and Atoms-In-Molecules (AIM) analysis. The shapes of these curves cannot be completely described by the standard exponential and power-law forms, but are well described by a threeparameter hybrid of the exponential and power-law forms. The r b -distance curves for covalent bonds tend to exhibit exponential behavior, while metallic bonds exhibit power-law behavior, and ionic bonds tend to exhibit a combination of the two. We next use a suite of both experimental and calculated (B3LYP/ Def2-TZVP) molecular structures of oxo-molecules, for which we could infer X-O bond valences of ~1 or ~2 v.u., combined with some crystal structure data, to estimate the curvature of the bond valencelength relationship in the high-valence region. Consistent with the results for the r b -distance curves, the standard forms of the bond valence-length equation become inadequate to describe high-valence bonds as they become more ionic. However, some of these systems demonstrate even higher curvature changes than our three-parameter hybrid form can manage. Therefore, we introduce a four-parameter hybrid form, and discuss possible reasons for the severe curvature. Although the addition of more parameters to the bond valence-length equation comes at a cost in terms of model simplicity and ease of optimization, they will be necessary to make the BVM useful for molecular systems and transition states.

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“…Information from such studies is therefore of high precision and relevance and provides in‐depth information on defined interactions between organic chemicals and soil constituents at an atomic and molecular level. Additionally, force‐field methods have been significantly improved and allow the investigation of larger systems including minerals (Gibbs et al , 2001). The ab initio methods are also very useful in characterizing the molecular properties of single organic chemicals (Novoszad et al , 2005), which can be related to sorption properties obtained in bench‐scale experiments.…”

Section: Introductionmentioning

confidence: 99%